Numerous quantitative models have been developed to simulate the long-term evolution of river basin topography. Most of these models reach an equilibrium state when the base level is lowered at a constant rate and the substrate and climate are constant in time. At equilibrium the erosion balances the base level lowering, so the topography remains frozen in time. However, some recent laboratory experiments contradict this behavior. In these experiments the space-time mean erosion rate balances the base level lowering rate, but the actual erosion rates are highly variable in space and time. Consequently, the channel networks are substantially mobile. The experimental flow conditions are approximately similar but not dynamically equivalent to those in nature, so it is unclear whether the observed dynamics are representative. This paper examines whether the processes occurring in the experiments produce basins that are geometrically similar to typical natural basins. To make this comparison, the conceptual framework of scaling invariance is used. Many similarities are observed, but we find that the experimental basins are slightly more elongated across a range of scales than the natural basins we consider and the relationship between channel slope and drainage area exhibits a break that is not found in the natural basins we analyze. In the experiments the slopes of small channels also depend on the proximity of large channels. This dependency is more pronounced for experiments with more mobile channel networks, and it is not observed in most of the natural basins we analyze.